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Concentration inequalities for stochastic differential equations of pure non-Poissonian jumps

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  • Torrisi, Giovanni Luca

Abstract

We provide concentration inequalities for solutions to stochastic differential equations of pure not-necessarily Poissonian jumps. Our proofs are based on transportation cost inequalities for square integrable functionals of point processes with stochastic intensity and elements of stochastic calculus with respect to semi-martingales. We apply the general results to solutions of stochastic differential equations driven by renewal and non-linear Hawkes point processes.

Suggested Citation

  • Torrisi, Giovanni Luca, 2020. "Concentration inequalities for stochastic differential equations of pure non-Poissonian jumps," Stochastic Processes and their Applications, Elsevier, vol. 130(10), pages 6445-6479.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:10:p:6445-6479
    DOI: 10.1016/j.spa.2020.05.017
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    References listed on IDEAS

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    1. Ma, Yutao, 2010. "Transportation inequalities for stochastic differential equations with jumps," Stochastic Processes and their Applications, Elsevier, vol. 120(1), pages 2-21, January.
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